Diffusion theory applied to tool-life stochastic modeling under a progressive wear process

In this paper a novel approach to the derivation of the tool-life distribution, when the tool useful life ends after a progressive wear process, is presented. It is based on the diffusion theory and exploits the Fokker-Planck equation. The Fokker-Planck coefficients are derived on the basis of the injury theory assumptions. That is, tool-wear occurs by detachment of small particles from the tool working surface, which are assumed to be identical and time-independent. In addition, they are supposed to be small enough to consider the detachment process as continuous. The tool useful life ends when a specified total volume of material is thus removed. Tool-life distributions are derived in two situations: (i) both Fokker-Planck coefficients are time-dependent only, and (ii) the diffusion coefficient is neglected and the drift is wear-dependent. Theoretical results are finally compared to experimental data concerning flank wear land in continuous turning of a C40 carbon steel bar adopting a P10 type sintered carbide insert. The adherence to the experimental data of the tool-life distributions derived exploiting the Fokker-Planck equation is satisfactory. Moreover, the tool-life distribution obtained when the diffusion coefficient is neglected and the drift is wear-dependent is able to well-represent the wear behavior at intermediate and later times.